The Nucleon Axial-Vector Form Factor at the Physical Point with the - - PowerPoint PPT Presentation
The Nucleon Axial-Vector Form Factor at the Physical Point with the HISQ Ensembles Aaron Meyer (asmeyer2012@uchicago.edu) University of Chicago/Fermilab May 1-2, 2015 USQCD All-Hands Meeting Fermilab Lattice/MILC Collaborations + Richard
Aaron Meyer (asmeyer2012@uchicago.edu) University of Chicago/Fermilab May 1-2, 2015 USQCD All-Hands Meeting Fermilab Lattice/MILC Collaborations + Richard Hill (UChicago) + Ruizi Li (Wuppertal) with support from URA Visiting Scholars Program, DOE SCGSR
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We will use MILC HISQ 2+1+1 ensembles at Mπ = 135 MeV with 3 lattice spacings Our primary objectives are to calculate:
As a byproduct, we will also get:
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Neutrino physics needs a better understanding of axial form factor:
systematic uncertainties and underestimates errors
models and nucleon form factors
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Nucleon-level/Nucleus-level effects entangled Measurements of observables are model-dependent LQCD acts as disruptive techology to break the cycle
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Most analyses assume the “Dipole form factor”: F dipole
A
(q2) = gA 1
m2
A
2 (1) Dipole is an ansatz: unmotivated in interesting energy range → uncontrolled systematics and underestimated uncertainties Essential to replace ansatz with model-independent ab-initio calculation from Lattice QCD MiniBooNE Collab., PHYS REV D 81, 092005 (2010)
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Aµ
⊥(q2) = Aµ(q2) − qµ
q2 q · A (2) FA
up(q)γµ
⊥γ5un(0) =
N′| ZAAa
⊥ µ
|N 0| ZAAa
0 (0) |πa ω2
0| 2 ˆ mPa (0) |πa Mπ
ω2
(3) Calculation applies for q2 = 0 without issue Renormalization cancels Will fit form factor using a model-independent parameterization: z(t; t0, tc) = √tc − t − √tc − t0 √tc − t + √tc − t0 FA(z) =
∞
anzn (4) As validated by B meson physics, only a few coefficients necessary to accurately represent data
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Other collaborations have at most one ensemble for one lattice spacing at physical pion mass (See backup slides for references)
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1 1 5 2 2 5 3 3 5
Mπ [MeV]
0.05 0.1 0.15 0.2
a (fm)
completed in progress planned Mπ=135 MeV 8 / 19
SU(2)I × GTS irrep #N #∆ 3
2, 8
2 3
2, 8′
2 3
2, 16
3 1
2, 8
1 1
2, 8′
1 1
2, 16
4 (J. A. Bailey) Group theory for staggered baryons is under control 3-point functions use same operator basis as 2-point functions Set of 4 operators to generate a 4 × 4 matrix of correlators for variational analysis Irrep 3
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Can get priors from fitting different taste ∆ states from 3
2, 8′
and 1
2, 8′
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(See last slide for references)
Doing as well as other calculations at physical masses MILC g − 2 proposal to generate a = 0.15 fm ensemble at larger L → can use for finite volume study Estimate finite-size effects with χPT and L¨ uscher methodology
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Will employ a number of techniques to remove excited states:
3-point function MILC Collaboration, R. Li offer expertise for many of these methods
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a ≈ 0.12 fm, mℓ
ms ≈ 0.16
a ≈ 0.09 fm, mℓ
ms ≈ 0.22
(R. Li, Ph.D. Thesis) Variational method has been tested/verified on HISQ Plateau after 3-4/4-5 timeslices → 3-point source/sink separation approximately 2× larger → Scaled with physical dimensions Excited states are under control
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≈ a N3
S × NT
Nconfs 8Nζ(Np + Nsink) fm M Jpsi-core-hr 0.15 323 × 48 1000 0.57 0.12 483 × 64 1000 4.71 0.09 643 × 96 1047 23.07 total 28.35 8 staggered baryon cube corners Nζ color vectors (using 3) Np momenta (using 3) Nsink sinks (source/sink separations) (using 2) = 120 inversions total per gauge configuration
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Neutrino physics is subject to underestimated and model-dependent systematics → To reduce systematics from modeling, need to understand nuclear physics → To understand nuclear physics, need to understand nucleon-level cross sections HISQ ensembles will produce a high-statistics calculation of the axial form factor at physical pion mass and provide a model-independent description of nucleon-level physics Other areas of study to address in the future to further the Fermilab neutrino program:
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Nuclear effects not well understood → Models which are best for one measurement are worst for another Need to break FA/nuclear model entanglement A νµ A′ p µ− (assumed mA = 0.99 GeV, reference hyperlinks online) NuWro Model RFG RFG+ assorted (χ2/DOF) [GENIE] TEM
leptonic(rate) 3.5 2.4 2.8-3.7 leptonic(shape) 4.1 1.7 2.1-3.8 hadronic(rate) 1.7[1.2] 3.9 1.9-3.7 hadronic(shape) 3.3[1.8] 5.8 3.6-4.8
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z-Expansion is a model-independent description of the axial form factor t = q2 = −Q2 tc = 9m2
π
z(t; t0, tc) = √tc − t − √tc − t0 √tc − t + √tc − t0 (5) FA(z) =
∞
anzn (6) Maps kinematically allowed region (t ≤ 0) to within z = ±1 From B meson physics, only a few coefficients necessary to accurately represent data z-Expansion implemented in GENIE, to be released soon [autumn]
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LBNE Experiment
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ETMC
PNDME
CSSM
χQCD Y.-B. Yang, M. Gong, K.-F. Liu, and M. Sun arXiv:1504.04052 [hep-ph] LHP(BMW)
urr et al. arXiv:1011.2711 [hep-lat] LHP(asqtad)
Institute of Technology (2010). LHP-RBC
RBC-UKQCD
UKQCD-QCDSF
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